Melissa Aldana Quartet (Friday and Thursday) A searching and self-assured young tenor saxophonist originally from Santiago, Chile, Melissa Aldana has earned the vocal support of Greg Osby, who released her most recent album, “Second Cycle,” on his Inner Circle label. On Friday she leads a trio with the bassist Pablo Menares and the drummer Greg Hutchinson; on Thursday she draws more directly from the album, with Mr. Menares, the trumpeter Gordon Au and the drummer Jochen Rueckert. Friday at 7:30, 9:30 and 11:30 p.m., Bar Next Door, 129 Macdougal Street, near West Third Street, Greenwich Village, (212) 529-5945, lalanternacaffe.com; $12 cover, with a one-drink minimum. Thursday at 9 and 10:30 p.m., Jazz Gallery at Salt Space, 1160 Broadway, fifth floor, at West 27th Street, (212) 242-1063, jazzgallery.org; $15, $10 for members in the first set; $10, $5 for members in the second set. (Nate Chinen)

Howard Alden and Warren Vaché (Thursday) Most present-day jazz traditionalists need no introduction to Mr. Alden, a nimble guitarist, or Mr. Vaché, a soulful cornetist. Both musicians are thoughtful stewards of swing, and their companionable history runs deep — reason enough to applaud this booking in one of the city’s cozier jazz rooms. At 8:30 and 10:30 p.m., Bar Next Door, 129 Macdougal Street, near West Third Street, Greenwich Village, (212) 529-5945, lalanternacaffe.com; $12 cover for each set, with a one-drink minimum. (Chinen)

Omer Avital & the Band of the East (Wednesday and Thursday) Mr. Avital, an Israeli bassist drawn to knockabout rhythm, has an engaging recent album, “Suite of the East” (Anzic), that reflects his global vision. His Band of the East typically includes Greg Tardy on tenor saxophone, Nadav Remez on guitar and Daniel Freedman on drums. From 9:30 p.m. to midnight, Smalls Jazz Club, 183 West 10th Street, West Village, (212) 252-5091, smallsjazzclub.com; $20 cover. (Chinen)

Patricia Barber Quartet (Thursday through Feb. 2) Ms. Barber’s verbosity and arch intellectualism are uncommon traits for a jazz singer, and she has sometimes been held at arm’s length by wary traditionalists. Her new album, “Smash” (Concord Jazz), won’t change that dynamic — see “Redshift,” a bossa nova that addresses the ups and downs of romance in the language of astrophysics — but it’s a good showcase for her talents, and for the working band that she brings here, featuring the guitarist John Kregor, the bassist Larry Kohut and the drummer Jon Deitemyer. At 7:30 and 9:30 p.m., Jazz Standard, 116 East 27th Street, Manhattan, (212) 576-2232, jazzstandard.net; $25, $30 next Friday and Saturday. (Chinen)

Jim Black Trio (Monday) Jim Black is known as a drummer of convulsive intensity and a bandleader rooted in the protocols of noise-rock. But on “Somatic” (Winter & Winter), his most recent album, he leads an acoustic trio much like this one, which has Teddy Klausner on piano and Chris Tordini on bass. Joining as a featured guest is the alto saxophonist Tim Berne, Mr. Black’s former bandleader in Bloodcount, a heavy-gauge fixture of the 1990s downtown scene. At 8 and 9 p.m., Shapeshifter Lab, 18 Whitwell Place, Park Slope, Brooklyn, shapeshifterlab.com; $10 cover. (Chinen)

Jane Ira Bloom Quartet (Sunday) Ms. Bloom, a soprano saxophonist with an exploratory ken, has committed to an all-ballads program in this engagement, though that hardly qualifies as a restriction for her. She’ll have responsive support from her rhythm section, with Dominic Fallacaro on piano, Cameron Brown on bass and Matt Wilson on drums. At 8:30 p.m., Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $10 cover, with a $10 minimum. (Chinen)

Cyrus Chestnut 50th Birthday Celebration (Friday through Sunday) Mr. Chestnut, a sure-footed pianist with a particular gift for gospel flourish, turned 50 last week. He is commemorating that milestone this week with his working quartet — featuring Stacey Dillard on saxophones, Dezron Douglas on bass and Neal Smith on drums — and as a special guest on Friday and Saturday only, the venerable tenor saxophonist Jimmy Heath. At 7:30 and 9:30 p.m., Dizzy’s Club Coca-Cola, Frederick P. Rose Hall, Jazz at Lincoln Center, 60th Street and Broadway, (212) 258-9595, jalc.org; $35 cover, $45 cover on Saturday, $15 for students at select sets, with a $10 minimum; some sets are sold out. (Chinen)

★ Jimmy Cobb Quartet (Friday and Saturday) The masterly hard-bop drummer Jimmy Cobb turned 84 last weekend; he continues his celebration on the bandstand, leading a quartet with the tenor saxophonist Javon Jackson, the pianist George Cables and the bassist John Webber. At 7, 9 and 10:30 p.m., Smoke, 2751 Broadway, at 106th Street, (212) 864-6662, smokejazz.com; $35 cover. (Chinen)

Bill Cunliffe Trio (Friday) An accomplished pianist and composer in the modern jazz mainstream, Bill Cunliffe doesn’t surface all that often here, having fruitfully established a home base in Los Angeles. For this one-nighter, he calls on the bassist Todd Coolman and the drummer John Riley, a reliable rhythm team. At 8 and 10 p.m., Kitano Hotel, 66 Park Avenue, at 38th Street, (212) 885-7119, kitano.com; $25 cover, with a $15 minimum. (Chinen)

Roman Filiu Quintet (Saturday) The alto saxophonist Roman Filiu has kept exalted company in and out of his homeland, Cuba — he apprenticed with both the pianist Chucho Valdés and the saxophonist David Murray — and he has recently been blazing his own trail through the New York scene. Drawing partly from “Musae” (World Culture Music), the assertively modern album he released last year, he leads a band that includes David Virelles on piano and Adam Rogers on guitar. At 9 and 10:30 p.m., Jazz Gallery at Salt Space, 1160 Broadway, fifth floor, at West 27th Street, (212) 242-1063, jazzgallery.org; $20, $10 for members. (Chinen)

★ Al Foster (Friday through Sunday) Mr. Foster has long been a drummer of laid-back locomotion, no less intense for sounding so casual. He’s been working at the Village Vanguard this week with an alert quartet that includes Eric Alexander on tenor saxophone, Adam Birnbaum on piano and Doug Weiss on bass. At 9 and 11 p.m., Village Vanguard, 178 Seventh Avenue South, at 11th Street, West Village, (212) 255-4037, villagevanguard.com; $25 cover, with a one-drink minimum. (Chinen)

GV3/TB3 Reinvented (Thursday) Two young bands with an abundance of composure, though their naming conventions could stand to be reconsidered. GV3, which plays at 8:30 p.m., is shorthand for Geoff Vidal Trio, led by Mr. Vidal, a tenor saxophonist from New Orleans, and featuring a flexible rhythm team of Linda Oh on bass and Colin Stranahan on drums. And TB3, performing at 10 p.m., stands for Tyler Blanton Trio, led by Mr. Blanton, a vibraphonist, and otherwise consisting here of Mr. Vidal, Mr. Stranahan and the bassist Matt Penman. (The arithmetic is iffy too.) At Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $10 for each, with a $10 minimum. (Chinen)

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Nicole Henry Quintet (Tuesday and Wednesday) Nicole Henry, a jazz singer of pop instinct and cabaret sophistication, celebrates the release of “So Good, So Right: Nicole Henry Live” (Banister). That album, recorded during an engagement at Feinstein’s at Loews Regency last year, features new arrangements of songs from the 1970s. At 7:30 and 9:30 p.m., Dizzy’s Club Coca-Cola, Frederick P. Rose Hall, Jazz at Lincoln Center, 60th Street and Broadway, (212) 258-9595, jalc.org; $35 cover, $15 for students at select sets, with a minimum of $10. (Chinen)

★ Vijay Iyer Trio (Friday through Sunday) The standout jazz album of 2012, at least by critical consensus, was “Accelerando” (ACT), a brilliant second effort from this aerodynamic trio. Led by the pianist Vijay Iyer and featuring the bassist Stephan Crump and the drummer Marcus Gilmore, the group strikes a balance of cleverly reframed cover tunes and vertiginously propulsive originals, finding endless traction in changeable rhythm. At 7:30 and 9:30 p.m., with an 11:30 set on Friday and Saturday, Jazz Standard, 116 East 27th Street, Manhattan, (212) 576-2232, jazzstandard.net; $30, $25 on Sunday. (Chinen)

Marc Johnson and Eliane Elias (Tuesday through Feb. 2) Mr. Johnson, a bassist of deeply sonorous style, and Ms. Elias, a pianist with a transparent touch and a fondness for subtle harmonic shading, recently released a lovely album together, “Swept Away” (ECM), with the saxophonist Joe Lovano and the drummer Joey Baron. For this engagement, the headliners, a husband-and-wife team, work with the veteran drummer Victor Lewis. At 8 and 10 p.m., Iridium Jazz Club, 1650 Broadway, at 51st Street, (212) 582-2121, theiridium.com; $35 cover, with a $10 minimum. (Chinen)

Nadje Noordhuis Quintet (Saturday) The trumpeter Nadje Noordhuis is probably best recognized for her role in Darcy James Argue’s Secret Society, though her self-titled recent debut on the Little Mystery label is slowly changing that. The album revolves around Ms. Noordhuis’s introspective compositions for a chamberlike ensemble that includes the violinist Sara Caswell, the classical guitarist Rupert Boyd and the bassist Joe Martin, all of whom rejoin her here. (Performing an opening set is the effervescent singer Jo Lawry, a featured vocalist on Sting’s recent tours.) At 7:30 p.m., Culture Project, 45 Bleecker Street, near Lafayette Street, East Village, (866) 811-4111, cultureproject.org; $20. (Chinen)

Linda Oh Quartet (Friday) As on her propulsive second album, “Initial Here” (Greenleaf), the bassist Linda Oh features her own compositions, and the occasional sacramental cover, for a slashing postbop quartet featuring the tenor saxophonist Dayna Stephens, the pianist Fabian Almazan and the drummer Rudy Royston. At 9 and 10:30 p.m., Jazz Gallery at Salt Space, 1160 Broadway, fifth floor, at West 27th Street, (212) 242-1063, jazzgallery.org; $20, $10 for members. (Chinen)

John Pizzarelli Quartet (Tuesday through Feb. 2) You may have spotted John Pizzarelli on television with Paul McCartney at last year’s Grammy Awards ceremony, playing music from the former Beatle’s standards album. It’s yet one more example — along with his own recent album, “Rockin’ in Rhythm: A Tribute to Duke Ellington” (Telarc) — of how Mr. Pizzarelli, a charismatic singer as well as a crisp guitarist, has solidified his stature as a modern exemplar of jazz-rooted cabaret. At 8:30 and 11 p.m., Birdland, 315 West 44th Street, Clinton, (212) 581-3080, birdlandjazz.com; $40 cover, with a $10 minimum. (Chinen)

Jason Rigby’s Cleveland-Detroit Trio (Saturday) The name of this group corresponds to its background: Mr. Rigby, a tenor saxophonist, hails from Cleveland, while his band mates, the bassist Cameron Brown and the drummer Gerald Cleaver, hail from Detroit. Their rapport is meant to reflect those origins, with earthiness and groove. At 9 and 10:30 p.m., Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $10 cover, with $10 minimum. (Chinen)

Diane Schuur (Tuesday through Feb. 3) A flinty and irrepressible jazz singer, Ms. Schuur has a new album, “Live,” that offers a fair indication of what she’ll deliver here, with a band organized by the pianist Alan Broadbent and featuring Joel Frahm on saxophones, Romero Lubambo on guitar, Ben Wolfe on bass and Ulysses Owens Jr. on drums. At 8 and 10:30 p.m., Blue Note, 131 West Third Street, Greenwich Village, (212) 475-8592, bluenote.net; $35 at tables, $20 at the bar, with a $5 minimum. (Chinen)

Omar Sosa and Paolo Fresu (Friday through Sunday) Mr. Sosa, a Cuban pianist and composer, and Mr. Fresu, an Italian trumpeter, have collaborated fruitfully before, notably on the 2011 album “Alma” (Ota), which flutters in the jet stream of global pop. They reprise their lyrical and worldly rapport here, with no additional accompaniment. At 8 and 10:30 p.m., Blue Note, 131 West Third Street, Greenwich Village, (212) 475-8592, bluenote.net; $25 at tables, $15 at the bar, with a $5 minimum. (Chinen)

Becca Stevens Band (Thursday) A vocalist and guitarist who balances deep melody against lyrical caprice, Ms. Stevens has been touring behind “Weightless,” a bright album released last fall on Sunnyside. Her working band, which seeks a folkloric flexibility, typically has Liam Robinson on accordion and piano, Chris Tordini on bass and Jordan Perlson on drums. At 8:30 p.m., Shapeshifter Lab, 18 Whitwell Place, Park Slope, Brooklyn, shapeshifterlab.com; $15 cover. (Chinen)

★ David Virelles and Continuum (Tuesday through Feb. 3) A freethinking young Cuban pianist, Mr. Virelles released one of last year’s best and most intriguing albums: “Continuum” (Pi), an ever-shifting amalgam of ancient folklore and avant-garde protocol. Next week Mr. Virelles presents this project at the Village Vanguard, where he has worked in bands led by the saxophonists Chris Potter and Mark Turner. He’ll have the same rhythm section as on the album: the bassist Ben Street, the percussionist-poet Román Díaz, the venerable drummer Andrew Cyrille. And on Thursday only, he’ll welcome a distinguished guest: the multi-reedist and composer Henry Threadgill. At 9 and 11 p.m., Village Vanguard, 178 Seventh Avenue South, at 11th Street, West Village, (212) 255-4037, villagevanguard.com; $25 cover, with a one-drink minimum. (Chinen)

Ben Williams and Sound Effect (Tuesday and Wednesday) As on “State of Art” (Concord), his polished recent debut, the bassist Ben Williams offers his portrait of modern jazz at the crossroads of pop and R&B, with help from the saxophonist Marcus Strickland, the guitarist Alex Wintz, the pianist Christian Sands and the drummer John Davis. At 7:30 and 9:30 p.m., Jazz Standard, 116 East 27th Street, Manhattan, (212) 576-2232, jazzstandard.net; $20 cover. (Chinen)